Note that the \(\lambda _6\)  term \(F_4 {\bar{F}}_5 \phi _3\)  in eq. (REF )
metamorphoses, using eq. (REF ), to \(\sin \omega F_4{\bar{F}}_5\phi _0\) , involving the inflaton field \(\phi _0\)  thus the \(\lambda _6\)  coupling becomes \(\sin \omega /\sqrt{2}\) . This is a highly desirable result, because as has been
found in Refs. [1]}, [2]} \(\lambda _6\)  should be \(\mathrel {\hbox{$<$}\hbox{$\sim $}}\) 10-3\( in order to provide appropriate reheating, baryogenesis and light neutrino masses. Thus \) 4/4\( should be \) <<1 \(, compatible with the F- and D-flat directions imposed constraints on the gauge singlets VEVs. Indeed, the following solution to the flatness conditions satisfy this requirement:{\begin{@align}{1}{-1}\overline{\phi }_4\sim \xi ^2\ ,\ \phi _-\sim \xi ^3\ ,\ \overline{\phi }_+\sim \xi ^3\ ,\ \end{@align}}and \) 4/410-3\(.This is compatible with (\ref {d1d5nr}) (due to the presence of the NR term) and (\ref {phibars}), provided \)453\( in order to satisfy (\ref {etl}).After applying (\ref {flata}), (\ref {dddd}) and (\ref {fPhi12})-(\ref {fhoc}) the D-flatness equations reduce to:{\begin{@align}{1}{-1}&\left|\phi _{45}\right|^2 -\frac{\left|T_3\right|^2}{2} \sim \xi ^2\,, \\&\left|\overline{\phi }_-\right|^2 + \left|{\phi }_+\right|^2 -\frac{\left|T_3\right|^2}{2} \sim \xi ^2\,,\\&\left|\Phi _{31}\right|^2-\frac{1}{2}\left(\left|D_1\right|^2 + \left|D_4\right|^2 - \left|D_5\right|^2\right)-\frac{1}{2} \left(\left|T_1\right|^2 + \left|T_3\right|^2 - \left|T_4\right|^2 \right)= 3\xi ^2\,,\\&2 \left|\phi _+\right|^2+\left|D_1\right|^2 + \left|D_4\right|^2 + \left|T_1\right|^2 - \left|T_4\right|^2 \sim 0\,,\end{@align}}which can be easily satisfied.\) section1-3.5ex plus-1ex minus-.2ex2.3ex plus.2exConclusions and outook
